Question

What is the volume of the cone to the nearest cubic millimeter? (Use ​π = 3.14)

A) 52 mm^3
B) 157 mm^3
C) 209 mm^3
D) 628 mm^3

Answer 1

C) 209 mm³

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

1. Brackets
2. Parenthesis
3. Exponents
4. Multiplication
5. Division
6. Addition
7. Subtraction

• Left to Right

Geometry

Volume of a Cone Formula:
`\displaystyle V = (1)/(3) \pi r^2h`

• r is radius
• h is height

Explanation:

Step 1: Define

Radius r = 5 mm

Height h = 8 mm

Step 2: Solve

1. Substitute in variables [Volume of a Cone Formula]:
   `\displaystyle V = (1)/(3) (3.14) (5 \ mm)^2(8 \ mm)`
2. [Volume] Evaluate exponents:
   `\displaystyle V = (1)/(3) (3.14) (25 \ mm^2)(8 \ mm)`
3. [Volume] Multiply:
   `\displaystyle V = (1.04667)(25 \ mm^2)(8 \ mm)`
4. [Volume] Multiply:
   `\displaystyle V = (26.1667 \ mm^2)(8 \ mm)`
5. [Volume] Multiply:
   `\displaystyle V = 209.333 \ mm^3`